| 一类拟三次系统的中心条件与极限环分支 |
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| 引用本文： | 赵百利,李险峰,曾志辉. 一类拟三次系统的中心条件与极限环分支[J]. 黑龙江科技学院学报, 2007, 17(3): 220-223 |
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| 作者姓名： | 赵百利 李险峰 曾志辉 |
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| 作者单位： | 1. 中南大学,数学科学与计算技术学院,长沙,410083
2. 兰州交通大学,非线性研究中心,兰州,730070 |
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| 基金项目： | 甘肃省自然科学基金 , 兰州交通大学校科研和教改项目 |
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| 摘 要： | 针对一类拟三次系统的中心条件与极限环分支问题,首先通过适当的变换将系统的原点(或无穷远点)转化为原点,然后求出该系统原点的前18个奇点量,从而导出原点成为中心和最高阶细焦点(细奇点)的条件.在此基础上给出了拟三次系统在原点分支出5个极限环的实例.这是首次讨论高于二次的拟解析系统分支出极限环的问题.
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| 关 键 词： | 拟三次系统 中心 极限环分支 三次系统 中心条件 极限环分支 cubic systems class bifurcation of limit cycles conditions 分支问题 解析系统 支出 奇点量 高阶细焦点 转化 无穷远点 变换 |
| 文章编号： | 1671-0118（2007）03-0220-04 |
| 修稿时间： | 2007-03-23 |
Center conditions and bifurcation of limit cycles for a class of quasi cubic systems |
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| ZHAO Baili,LI Xianfeng,ZENG Zhihui. Center conditions and bifurcation of limit cycles for a class of quasi cubic systems[J]. Journal of Heilongjiang Institute of Science and Technology, 2007, 17(3): 220-223 |
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| Authors: | ZHAO Baili LI Xianfeng ZENG Zhihui |
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| Affiliation: | 1.Institute of Mathematical Science and Computing Technique, Central South University, Changsha 410083, China; 2. Nonlinear Science Research Center, Lanzhou Jiaotnng University, Lanzhou 730070, China |
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| Abstract: | In this paper, the center conditions and bifurcation of limit cycles for a class of quasi cubic systems are investigated. Firstly, the eighteen singular point quantities are computed and conditions for origin to be a center are deduced as well, then a system that bifurcates five limit cycles at the origin is constructed. As far as we know, this is the first time that the problem of limit cycles bifurcated from a class of quasi systems whose degree is higher than two. |
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| Keywords: | quasi cubic system centers bifurcation of limit cycles |
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